Problem: Rewrite as a simplified fraction. ${3.34\overline{8} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3348.8888...\\ 100x &= 334.8888...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3014}$ ${x = \dfrac{3014}{900}} $ ${x = \dfrac{1507}{450}} \text{or} {3 \dfrac{157}{450}}$